package org.matheclipse.core.integrate.rubi45;


import static org.matheclipse.core.expression.F.*;
import static org.matheclipse.core.integrate.rubi45.UtilityFunctionCtors.*;
import static org.matheclipse.core.integrate.rubi45.UtilityFunctions.*;
import org.matheclipse.core.interfaces.IAST;

/** 
 * IndefiniteIntegrationRules from the <a href="http://www.apmaths.uwo.ca/~arich/">Rubi -
 * rule-based integrator</a>.
 *  
 */
public class IntRules76 { 
  public static IAST RULES = List( 
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(C_DEFAULT,Sqr($($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Times(B_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_DEFAULT),Power(Times(d_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_DEFAULT)),x_Symbol),
    Condition(Plus(Times(CSymbol,d,Tan(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),Plus(m,C1)),Power(Times(d,Sec(Plus(e,Times(f,x)))),Plus(n,Negate(C1))),Power(Times(b,f,Plus(m,n,C1)),-1)),Times(d,Power(Times(b,Plus(m,n,C1)),-1),Int(Times(Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),m),Power(Times(d,Sec(Plus(e,Times(f,x)))),Plus(n,Negate(C1))),Simp(Plus(Times(a,CSymbol,Plus(n,Negate(C1))),Times(Plus(Times(ASymbol,b,Plus(m,n,C1)),Times(b,CSymbol,Plus(m,n))),Sec(Plus(e,Times(f,x)))),Times(Plus(Times(b,BSymbol,Plus(m,n,C1)),Times(CN1,a,CSymbol,n)),Sqr(Sec(Plus(e,Times(f,x)))))),x)),x))),And(And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol,CSymbol,m),x),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))),RationalQ(n)),Greater(n,C0)))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(C_DEFAULT,Sqr($($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Times(B_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_DEFAULT),Power(Times(d_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_DEFAULT)),x_Symbol),
    Condition(Plus(Times(CN1,CSymbol,d,Cot(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),Plus(m,C1)),Power(Times(d,Csc(Plus(e,Times(f,x)))),Plus(n,Negate(C1))),Power(Times(b,f,Plus(m,n,C1)),-1)),Times(d,Power(Times(b,Plus(m,n,C1)),-1),Int(Times(Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),m),Power(Times(d,Csc(Plus(e,Times(f,x)))),Plus(n,Negate(C1))),Simp(Plus(Times(a,CSymbol,Plus(n,Negate(C1))),Times(Plus(Times(ASymbol,b,Plus(m,n,C1)),Times(b,CSymbol,Plus(m,n))),Csc(Plus(e,Times(f,x)))),Times(Plus(Times(b,BSymbol,Plus(m,n,C1)),Times(CN1,a,CSymbol,n)),Sqr(Csc(Plus(e,Times(f,x)))))),x)),x))),And(And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol,CSymbol,m),x),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))),RationalQ(n)),Greater(n,C0)))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(C_DEFAULT,Sqr($($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_DEFAULT),Power(Times(d_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_DEFAULT)),x_Symbol),
    Condition(Plus(Times(CSymbol,d,Tan(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),Plus(m,C1)),Power(Times(d,Sec(Plus(e,Times(f,x)))),Plus(n,Negate(C1))),Power(Times(b,f,Plus(m,n,C1)),-1)),Times(d,Power(Times(b,Plus(m,n,C1)),-1),Int(Times(Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),m),Power(Times(d,Sec(Plus(e,Times(f,x)))),Plus(n,Negate(C1))),Simp(Plus(Times(a,CSymbol,Plus(n,Negate(C1))),Times(Plus(Times(ASymbol,b,Plus(m,n,C1)),Times(b,CSymbol,Plus(m,n))),Sec(Plus(e,Times(f,x)))),Times(CN1,a,CSymbol,n,Sqr(Sec(Plus(e,Times(f,x)))))),x)),x))),And(And(And(FreeQ(List(a,b,d,e,f,ASymbol,CSymbol,m),x),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))),RationalQ(n)),Greater(n,C0)))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(C_DEFAULT,Sqr($($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_DEFAULT),Power(Times(d_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_DEFAULT)),x_Symbol),
    Condition(Plus(Times(CN1,CSymbol,d,Cot(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),Plus(m,C1)),Power(Times(d,Csc(Plus(e,Times(f,x)))),Plus(n,Negate(C1))),Power(Times(b,f,Plus(m,n,C1)),-1)),Times(d,Power(Times(b,Plus(m,n,C1)),-1),Int(Times(Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),m),Power(Times(d,Csc(Plus(e,Times(f,x)))),Plus(n,Negate(C1))),Simp(Plus(Times(a,CSymbol,Plus(n,Negate(C1))),Times(Plus(Times(ASymbol,b,Plus(m,n,C1)),Times(b,CSymbol,Plus(m,n))),Csc(Plus(e,Times(f,x)))),Times(CN1,a,CSymbol,n,Sqr(Csc(Plus(e,Times(f,x)))))),x)),x))),And(And(And(FreeQ(List(a,b,d,e,f,ASymbol,CSymbol,m),x),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))),RationalQ(n)),Greater(n,C0)))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(C_DEFAULT,Sqr($($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Times(B_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Times(d_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Plus(Times(CN1,ASymbol,Tan(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),Plus(m,C1)),Power(Times(d,Sec(Plus(e,Times(f,x)))),n),Power(Times(a,f,n),-1)),Times(Power(Times(a,d,n),-1),Int(Times(Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),m),Power(Times(d,Sec(Plus(e,Times(f,x)))),Plus(n,C1)),Simp(Plus(Times(a,BSymbol,n),Times(CN1,ASymbol,b,Plus(m,n,C1)),Times(a,Plus(ASymbol,Times(ASymbol,n),Times(CSymbol,n)),Sec(Plus(e,Times(f,x)))),Times(ASymbol,b,Plus(m,n,C2),Sqr(Sec(Plus(e,Times(f,x)))))),x)),x))),And(And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol,CSymbol,m),x),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))),RationalQ(n)),LessEqual(n,CN1)))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(C_DEFAULT,Sqr($($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Times(B_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Times(d_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Plus(Times(ASymbol,Cot(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),Plus(m,C1)),Power(Times(d,Csc(Plus(e,Times(f,x)))),n),Power(Times(a,f,n),-1)),Times(Power(Times(a,d,n),-1),Int(Times(Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),m),Power(Times(d,Csc(Plus(e,Times(f,x)))),Plus(n,C1)),Simp(Plus(Times(a,BSymbol,n),Times(CN1,ASymbol,b,Plus(m,n,C1)),Times(a,Plus(ASymbol,Times(ASymbol,n),Times(CSymbol,n)),Csc(Plus(e,Times(f,x)))),Times(ASymbol,b,Plus(m,n,C2),Sqr(Csc(Plus(e,Times(f,x)))))),x)),x))),And(And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol,CSymbol,m),x),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))),RationalQ(n)),LessEqual(n,CN1)))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(C_DEFAULT,Sqr($($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Times(d_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Plus(Times(CN1,ASymbol,Tan(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),Plus(m,C1)),Power(Times(d,Sec(Plus(e,Times(f,x)))),n),Power(Times(a,f,n),-1)),Times(Power(Times(a,d,n),-1),Int(Times(Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),m),Power(Times(d,Sec(Plus(e,Times(f,x)))),Plus(n,C1)),Simp(Plus(Times(CN1,ASymbol,b,Plus(m,n,C1)),Times(a,Plus(ASymbol,Times(ASymbol,n),Times(CSymbol,n)),Sec(Plus(e,Times(f,x)))),Times(ASymbol,b,Plus(m,n,C2),Sqr(Sec(Plus(e,Times(f,x)))))),x)),x))),And(And(And(FreeQ(List(a,b,d,e,f,ASymbol,CSymbol,m),x),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))),RationalQ(n)),LessEqual(n,CN1)))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(C_DEFAULT,Sqr($($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Times(d_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Plus(Times(ASymbol,Cot(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),Plus(m,C1)),Power(Times(d,Csc(Plus(e,Times(f,x)))),n),Power(Times(a,f,n),-1)),Times(Power(Times(a,d,n),-1),Int(Times(Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),m),Power(Times(d,Csc(Plus(e,Times(f,x)))),Plus(n,C1)),Simp(Plus(Times(CN1,ASymbol,b,Plus(m,n,C1)),Times(a,Plus(ASymbol,Times(ASymbol,n),Times(CSymbol,n)),Csc(Plus(e,Times(f,x)))),Times(ASymbol,b,Plus(m,n,C2),Sqr(Csc(Plus(e,Times(f,x)))))),x)),x))),And(And(And(FreeQ(List(a,b,d,e,f,ASymbol,CSymbol,m),x),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))),RationalQ(n)),LessEqual(n,CN1)))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(C_DEFAULT,Sqr($($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Times(B_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Times(Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Sqrt(Times(d_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))))),-1)),x_Symbol),
    Condition(Plus(Times(Plus(Times(ASymbol,Sqr(b)),Times(CN1,a,b,BSymbol),Times(Sqr(a),CSymbol)),Power(Times(Sqr(a),Sqr(d)),-1),Int(Times(Power(Times(d,Sec(Plus(e,Times(f,x)))),QQ(3L,2L)),Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),-1)),x)),Times(Power(a,-2),Int(Times(Plus(Times(a,ASymbol),Times(CN1,Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)),Sec(Plus(e,Times(f,x))))),Power(Times(d,Sec(Plus(e,Times(f,x)))),CN1D2)),x))),And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol,CSymbol),x),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(C_DEFAULT,Sqr($($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Times(B_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Times(Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Sqrt(Times(d_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))))),-1)),x_Symbol),
    Condition(Plus(Times(Plus(Times(ASymbol,Sqr(b)),Times(CN1,a,b,BSymbol),Times(Sqr(a),CSymbol)),Power(Times(Sqr(a),Sqr(d)),-1),Int(Times(Power(Times(d,Csc(Plus(e,Times(f,x)))),QQ(3L,2L)),Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),-1)),x)),Times(Power(a,-2),Int(Times(Plus(Times(a,ASymbol),Times(CN1,Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)),Csc(Plus(e,Times(f,x))))),Power(Times(d,Csc(Plus(e,Times(f,x)))),CN1D2)),x))),And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol,CSymbol),x),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(C_DEFAULT,Sqr($($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))))),Power(Times(Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Sqrt(Times(d_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))))),-1)),x_Symbol),
    Condition(Plus(Times(Plus(Times(ASymbol,Sqr(b)),Times(Sqr(a),CSymbol)),Power(Times(Sqr(a),Sqr(d)),-1),Int(Times(Power(Times(d,Sec(Plus(e,Times(f,x)))),QQ(3L,2L)),Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),-1)),x)),Times(Power(a,-2),Int(Times(Plus(Times(a,ASymbol),Times(CN1,ASymbol,b,Sec(Plus(e,Times(f,x))))),Power(Times(d,Sec(Plus(e,Times(f,x)))),CN1D2)),x))),And(FreeQ(List(a,b,d,e,f,ASymbol,CSymbol),x),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(C_DEFAULT,Sqr($($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))))),Power(Times(Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Sqrt(Times(d_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))))),-1)),x_Symbol),
    Condition(Plus(Times(Plus(Times(ASymbol,Sqr(b)),Times(Sqr(a),CSymbol)),Power(Times(Sqr(a),Sqr(d)),-1),Int(Times(Power(Times(d,Csc(Plus(e,Times(f,x)))),QQ(3L,2L)),Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),-1)),x)),Times(Power(a,-2),Int(Times(Plus(Times(a,ASymbol),Times(CN1,ASymbol,b,Csc(Plus(e,Times(f,x))))),Power(Times(d,Csc(Plus(e,Times(f,x)))),CN1D2)),x))),And(FreeQ(List(a,b,d,e,f,ASymbol,CSymbol),x),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(C_DEFAULT,Sqr($($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Times(B_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Times(Sqrt(Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))))),Sqrt(Times(d_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))))),-1)),x_Symbol),
    Condition(Plus(Times(CSymbol,Power(d,-2),Int(Times(Power(Times(d,Sec(Plus(e,Times(f,x)))),QQ(3L,2L)),Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),CN1D2)),x)),Int(Times(Plus(ASymbol,Times(BSymbol,Sec(Plus(e,Times(f,x))))),Power(Times(Sqrt(Times(d,Sec(Plus(e,Times(f,x))))),Sqrt(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))))),-1)),x)),And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol,CSymbol),x),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(C_DEFAULT,Sqr($($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Times(B_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Times(Sqrt(Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))))),Sqrt(Times(d_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))))),-1)),x_Symbol),
    Condition(Plus(Times(CSymbol,Power(d,-2),Int(Times(Power(Times(d,Csc(Plus(e,Times(f,x)))),QQ(3L,2L)),Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),CN1D2)),x)),Int(Times(Plus(ASymbol,Times(BSymbol,Csc(Plus(e,Times(f,x))))),Power(Times(Sqrt(Times(d,Csc(Plus(e,Times(f,x))))),Sqrt(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))))),-1)),x)),And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol,CSymbol),x),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(C_DEFAULT,Sqr($($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))))),Power(Times(Sqrt(Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))))),Sqrt(Times(d_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))))),-1)),x_Symbol),
    Condition(Plus(Times(CSymbol,Power(d,-2),Int(Times(Power(Times(d,Sec(Plus(e,Times(f,x)))),QQ(3L,2L)),Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),CN1D2)),x)),Times(ASymbol,Int(Power(Times(Sqrt(Times(d,Sec(Plus(e,Times(f,x))))),Sqrt(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))))),-1),x))),And(FreeQ(List(a,b,d,e,f,ASymbol,CSymbol),x),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(C_DEFAULT,Sqr($($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))))),Power(Times(Sqrt(Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))))),Sqrt(Times(d_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))))),-1)),x_Symbol),
    Condition(Plus(Times(CSymbol,Power(d,-2),Int(Times(Power(Times(d,Csc(Plus(e,Times(f,x)))),QQ(3L,2L)),Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),CN1D2)),x)),Times(ASymbol,Int(Power(Times(Sqrt(Times(d,Csc(Plus(e,Times(f,x))))),Sqrt(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))))),-1),x))),And(FreeQ(List(a,b,d,e,f,ASymbol,CSymbol),x),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(C_DEFAULT,Sqr($($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Times(B_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Times(d_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Integrate(Times(Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),m),Power(Times(d,Sec(Plus(e,Times(f,x)))),n),Plus(ASymbol,Times(BSymbol,Sec(Plus(e,Times(f,x)))),Times(CSymbol,Sqr(Sec(Plus(e,Times(f,x))))))),x),And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol,CSymbol,m,n),x),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(C_DEFAULT,Sqr($($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Times(B_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Times(d_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Integrate(Times(Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),m),Power(Times(d,Csc(Plus(e,Times(f,x)))),n),Plus(ASymbol,Times(BSymbol,Csc(Plus(e,Times(f,x)))),Times(CSymbol,Sqr(Csc(Plus(e,Times(f,x))))))),x),And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol,CSymbol,m,n),x),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(C_DEFAULT,Sqr($($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Times(d_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Integrate(Times(Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),m),Power(Times(d,Sec(Plus(e,Times(f,x)))),n),Plus(ASymbol,Times(CSymbol,Sqr(Sec(Plus(e,Times(f,x))))))),x),And(FreeQ(List(a,b,d,e,f,ASymbol,CSymbol,m,n),x),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(C_DEFAULT,Sqr($($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Times(d_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Integrate(Times(Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),m),Power(Times(d,Csc(Plus(e,Times(f,x)))),n),Plus(ASymbol,Times(CSymbol,Sqr(Csc(Plus(e,Times(f,x))))))),x),And(FreeQ(List(a,b,d,e,f,ASymbol,CSymbol,m,n),x),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b)))))))
  );
}
